I have spent much of my career working to bring abstract linear algebra and practical matrix computation closer together. This project is my latest effort.... read more >>

(I have a guest blogger today. Ron Jones worked with me in 1985 for his Ph. D. from the University of New Mexico. He retired recently after nearly 40 years at Sandia National Labs in Albuquerque and now has a chance to return to the problem he studied in his thesis. -- CBM)... read more >>

I have just returned from a one-day workshop at U. C. Santa Barbara honoring John Gilbert on his 70th birthday and his official retirement after 20 years on the UCSB faculty.... read more >>

I recently had an opportunity to chat with Ernie, the Large Language Model currently under development at the Chinese internet search giant, Baidu. As I expected, Ernie's responses are in Chinese. I don't speak Chinese, so I have asked Google Translate for the response in English.... read more >>

While it is still fresh in my mind, I want to describe the conversation I had with a publicly available version of ChatGPT, the much-discussed large language model, LLM, for conversational artificial intelligence.... read more >>

Christian Reinsch and Roland Bulirsch both passed away recently, Reinsch on October 8 and Bulirsch on September 21. Reinsch was 88 years old and Bulirsch was 89. Both of them were retired professors of numerical analysis at the Technical University of Munich. Both of them were friends of mine. But in almost all other ways, they were very different people.... read more >>

I do not recall having seen this matrix before, but I will not be surprised to learn that somebody else already knows all about it, especially if that person's name is Nick.... read more >>

My recent obsession with cubes in this blog has led me back to Rubik's cube, perhaps the greatest mathematical puzzle of all time.... read more >>

The Menger sponge is a popular fractal that generalizes Cantor sets and Sierpinski triangles. Its fractal dimension is between two and three.... read more >>

Quaternions are generalizations of the complex numbers that have found applications in computer graphics and many other fields.... read more >>